Research Projects

The project aims to study the boundedness properties of the bilinear Bochner Riesz operators on convex domains in the plane. The bilinear Kakeya maximal function arises naturally in the study of such operators; we are also interested in studying its boundedness in dimensions greater than two. We will also consider the uncentered analogue of the bilinear spherical maximal function. Another important aspect of this project is the study of boundedness of single-scale averages and maximal functions of bilinear Radon transform that exhibits modulation invariance property similar to that of the well-studied bilinear Hilbert transform.